Search a number
modest n.  and  untouchable n.

First numbers that belong to both sets:

206, 406, 818, 836, 872, 1222, 1236, 1254, 1266, 1418, 1422, 1822, 1866, 2022, 2036, 2436, 2454, 3236, 3266, 3296, 3666, 4018, 4036, 4072, 4088, 4148, 4854, 5278, 5666, 6018, 8024, 8036, 8108, 10054, 10074, 10222, 12036, 12054, 12444, 12666, 14018, 14126, 14518, 16018, 16108, 16296, 18054, 18222, 20006, 20018, 20060, 24148, 24222, 24666, 26078, 26222, 28108, 28252, 28378, 30222, 30666, 32036, 32048, 32108, 32222, 32864, 34074, 34102, 34222, 34918, 36324, 36444, 36666, 38342, 40036, 40044, 40060, 40072, 40222, 40296, 40370, 40404, 42378, 42518, 44066, 44148, 44198, 48054, 48072, 48148, 48216, 48324, 48432, 48888, 50370, 50666, 52078, 52108, 52702, 54074, 54162, 54222, 54486, 56072, 56108, 56148, 56216, 56222, 56518, 56756, 58222, 60022, 60180, 60198, 60222, 60270, 62558, 64074, 64108, 64148, 64222, 64288, 64296, 64432, 64864, 64888, 65454, 66198, 66666, 68108, 68306, 70270, 70518, 72108, 72216, 72296, 72324, 72486, 72972, 74666, 76342, 76684, 78222, 78702, 78962, 80018, 80036, 80120, 80132, 80202, 80216, 80270, 80720, 81212, 82738, 84108, 84126, 84162, 84252, 84518, 84666, 87272, 88198, 88296, 90162, 90666, 92148, 92276, 94846, 96144, 96148, 96288, 96666, 96888, 98294, 98882, 100148, 100202, 100370, 102222, 102306, 102666, 103030, 104156, 104216, 104468, 104666, 108666, 110198, 110370, 112126, 112148, 112222, 112296, 112518, 112756, 114666, 116148, 116222, 120036, 120054, 120108, 120132, 120162, 120180, 120198, 120222, 120270, 120370, 120444, 120594, 120606, 120666, 120810, 121188, 123636, 124222, 124372, 126162, 126222, 126486, 126666, 128296, 128384, 130666, 130962, 132162, 132222, 132444, 136148, 136204, 136296, 136918, 138162, 138414, 138666, 140022, 140066, 140148, 140202, 140740, 141386, 142222, 142426, 144148, 144216, 144222, 144296, 144432, 144444, 144648, 148222, 152228, 152342, 152456, 154222, 154378, 154518, 156162, 156666, 156702, 156962, 160018, 160024, 160044, 160048, 160072, 160176, 160270, 160288, 160432, 160480, 160720, 160888, 161616, 162486, 164246, 164738, 164848, 166498.

Some larger examples :